"Ere" is an old-fashioned word meaning "before." So the speaker is referring to those moments before he is bound by slumber's chains, i.e. before he falls asleep. And in those moments in the stillness of the night the speaker's mind is flooded with memories, both happy and sad, of the laughter and tears of his boyhood years.

He then goes on to reflect ruefully on the fact that so many of his dear friends have passed away, leaving him feeling so incredibly alone, as if he's walking all by himself in a deserted banquet hall where all the lights have gone out. As the speaker's friends are all long since gone, such darkness can only be illuminated by his memories of them, the shining light of happier times.

In this poem, Moore writes about the thoughts and memories that crowd his mind before he falls asleep at night. The phrase in question means that these memories come to him before--"ere"--he falls asleep--in other words, before "slumber" overtakes him. When he says sleep or slumber's chain has bound him, he refers to the way sleep holds us in place and controls our thoughts. What Moore focuses on is the liminal space between being absorbed by all the worries and tasks of daily life and being "dead to the world" in sleep.

In those moments before sleep, the past comes flooding into Moore's mind. At first, good--"fond"-- memories of his boyhood come back to him. But then, as he remembers how heartbreak and death have hit people he knew in happier days, the memories become darker. 

In the second stanza, he likens the friends he once knew, all linked together as if to one tree, to fallen leaves. The old days are gone and won't come back, so "sad memory" fills the poet's mind until he drifts off into slumber's chains.